Problem: Solve for $x$ and $y$ using elimination. ${5x-3y = 3}$ ${-4x-5y = -32}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-3$ ${25x-15y = 15}$ $12x+15y = 96$ Add the top and bottom equations together. $37x = 111$ $\dfrac{37x}{{37}} = \dfrac{111}{{37}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {5x-3y = 3}\thinspace$ to find $y$ ${5}{(3)}{ - 3y = 3}$ $15-3y = 3$ $15{-15} - 3y = 3{-15}$ $-3y = -12$ $\dfrac{-3y}{{-3}} = \dfrac{-12}{{-3}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {-4x-5y = -32}\thinspace$ and get the same answer for $y$ : ${-4}{(3)}{ - 5y = -32}$ ${y = 4}$